Two days tour outside Beijing
Q: I've two free days in Beijing area and I've been in the clasic tourist areas, Great Wall . . ., any sugestions for first week of november? other city? Thanks.
One possibility is Chengde Summer Resort (Chengde Bishu Shanzhuan). The imperial resort was built in the 18th century, during the Qing dynasty. You can tour the palace, do a boat ride on the lake, and visit the Buddhist temples that scatter around in the region. The park is 200 km northeast of Beijing; by coach it is a ride of 4 hours.
For a day trip, Tianjin is another possibility. Tianjin is actually one of the largest cities in China, one of the four cities directly governed by the central government, but in recent decades it has been overshadowed by Beijing because of it's adjacent to the national capital. The city started as a crossing and trade port on Haihe River and used to be known for the foreign settlements in the city. Among the attractions there are the old settle quarters, Guwenhua Jie (Ancient Culture Street - antiques, art, etc), and Meishijie (Restaurant Street). Connected now to Beijing by high-speed train, it is just a ride of 30 minutes from Beijing Southern Railway Station to Tianjin Railway Station. One day there is enough time to get around and return to Beijing.
There are many smaller resorts in the suburbs of Beijing, which can be destinations of a trip of one or two days. No historical sites, no dramatic scenes, but pleasant places for retreats, with hills, lakes, and farmers' meals. There are many of such places, such as Yunmeng Shan (Mt. Yunmeng), Yesanpo (Three Wild Slopes), Longqing Xia (Longqing Valley), Qinglong Xia (Qinglong Valley), Jingdong Daxiagu (East Beijing Valley)... These are developed tourist areas, so you're not going into true wilderness, for better or worse. If you plan to visit one of these places, one issue is how to go. Are you going as a part of a group, by hiring a car along with an interpreter? Unlike with major tourist destinations, people going to these places are mostly local.
There are many smaller retreat areas in the suburbs of Beijing
But for the fact that you're traveling in November, Baidaihe would have been another possibility - it is a train ride of 3 hours from Beijing. This is a summer resort, with beach as its main attraction, along with Shanhaiguan (Mountain and Sea Gate, the eastern end of the Great Wall). Not much else to do if you cannot go to the sea.
If you really try, you can probably pack in another city that is a bit farther away from Beijing. For example, you can probably do a two day tour of a city such as Xian very quickly. Fly in the night before and fly out the seconding evening. On the first day you visit the Terracotta Warriors of the First Qin Emperor outside the city and tour the sites in Xian (Great Goose Pagoda, the city wall, etc.). This is doable if you plan everything very tightly, but it is really a rush for a tour destination such as Xian. It depends on your circumstances - Will there be another opportunity for you to do a more leisurely tour? Will you miss your international flight if something does not work out as smoothly you have thought? It would be easier for a native person than for a foreign traveler to pull this off. Of course, if you one does want to do something like a quick tour of Xian in two days, there are few cities in China of with which you cannot do this. Just remember you'll be rushing along instead of having a leisurely vacation and there are risks - if something does not work out, your trip may not come off so well. Staying close to Beijing may be the best thing to do.